Games add mods when they need them, and they are usually added by trusted members of the community and/or runners of the game.
Unless you're asking how to get mod for a game that currently doesn't have an active moderator. You can request that through a thread in The Site forum (please read all rules in the OP to make sure you comply with everything).
DM the current supermods (red sword). Please make sure you are familiar with he moderation rules and know how to properly retime runs. Please do not ask more than once or harass mods if they do not add you, and do not ask to become mod for games you don't actively run. Mods should be knowledgeable and trustworthy community members. You'll likely be added as a verifier first, and if you participate in the community for a long time, you'll eventually be upped to a mod, and maybe a super.
Considering you have no runs on your account, I’m going to suggest not worrying about becoming a mod right now. Just pick a game or two to start running and maybe you’ll eventually be able to moderate one of them.